Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Project Lead The Way® Copyright 2006

Physical Property Analysis Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Physical Property Analysis Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Physical Properties A physical property is a property that can be observed or measured without changing the identity of the matter. Examples of Physical Properties: Volume Density Color Surface Area Centroid Moment of Inertia Mass Odor Temperature Melting Point Viscosity Electric Charge Project Lead The Way® Copyright 2006

Physical Property Analysis Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Physical Property Analysis The size, volume, surface area, and other properties associated with a solid model are often part of the design constraints or solution criteria. The following are physical properties presented in typical solid modeling programs: Volume Density Mass Surface Area Center of Gravity Moment of Inertia Product of Inertia Radii of Gyration Principal Axes Principal Moments Length Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Physical Properties In this lesson you will investigate the following physical properties: Volume Surface Area Density Mass Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Volume Volume is the amount of three-dimensional space occupied by an object or enclosed within a container Design engineers use volume to determine the amount of material needed to produce a part Different formulas for different shapes The teacher may want to supplement student knowledge about the use of formulas and related mathematical properties using variables. 8 4 Rectangular Prism V = H x W x L V = 4” x 4” x 8” V = 128 in.3 Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Volume in Cubic Units Measure volume using cubic units: Cubic inches (in.3) Cubic feet (ft3) Cubic yards (yds3) Cubic centimeters (cm3) Cubic meters (m3) It is imperative to keep your units the same when measuring and calculating volume. Project Lead The Way® Copyright 2006

Volume Formulas for Prisms, Cylinders, Pyramids, or Cones Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Volume Formulas for Prisms, Cylinders, Pyramids, or Cones If B is the area of the base of a prism, cylinder, pyramid, or cone and H is the height of the solid, then the formula for the volume is V = BH Note: You will need to calculate the area of the shape for the base of the prism. For example: If the solid is a triangular prism, then you will need to calculate the area of the triangle for the base and then calculate the volume. Project Lead The Way® Copyright 2006

Area Formulas for Bases of Prisms, Cylinders, and Pyramids Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Area Formulas for Bases of Prisms, Cylinders, and Pyramids Rectangular Prism – base is rectangle, therefore A = length * width or A = lw Cylinder – base is a circle, therefore A = pi * radius of circle squared or A = πr2 Square Pyramid – base is a square, therefore A = length * width or A = lw or side squared since the sides are the same on a square or A = s2 Project Lead The Way® Copyright 2006

Volume of a Cone A Special Case Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Volume of a Cone A Special Case A cone is 1/3 of a cylinder The base of a cylinder is a circle The area of a circle is A=πr2 Therefore, the formula for the volume of a cone is V= 1/3Ah where A=πr2 and h is the height of the cone Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Density Density is defined as mass per unit volume. Density is different for every material and can be found in a machinist handbook. Density is always provided, either by looking in a machinist handbook or from tables provided in 3D modeling software. Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Mass Mass is the amount of matter in an object or the quantity of the inertia of the object. Many materials are purchased by weight; to find weight, you need to know the mass. Polypropylene has a density of .035 lb/in.3 and Mass = Volume x Density Explain to students that the units for the inches cubed are cancelled out through division. Since there are inches cubed in the numerator and inches cubed in the denominator, they equal one. One times pounds leaves pounds. Mass = 128 in.3 x .035 lb/in.3 Mass = 4.48 lb Using the volume from the previous example: V = 128 in.3 Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Surface Area Surface area is the squared dimensions of the exterior surface. Surface area is important when determining coatings and heat transfer of a part. A= 4in. x 4in. = 16 in.2 B= 4in. x 8in. = 32 in.2 C= 4in. x 8in. = 32 in.2 D= 4in. x 8in. = 32 in.2 E= 4in. x 8in. = 32 in.2 F= 4in. x 4in. = 16 in.2 B C D E F A A + B+ C + D+ E + F = 160 in.2 Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis To start the Mass Property function, right click the solid model name in the Browser. Pick Properties Mass Property values will be used for predicting material quantity needed for production, finishing, packaging, and shipping. Project Lead The Way® Copyright 2006

Additional Physical Properties Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Additional Physical Properties Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Center of Gravity A 3D point where the total weight of the body may be considered to be concentrated. The average location of an object. If an object rotates when thrown it rotates about its center of gravity. An object can be balance on a sharp point placed directly beneath its center of gravity Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Centroid A 3D point defining the geometric center of a solid. Do not confuse centroid with the center of gravity. The two only exist at the same 3D point when the part has uniform geometry and density. Project Lead The Way® Copyright 2006

Mass Property Analysis Principal Axes Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis The lines of intersection created from three mutually perpendicular planes, with the three planes’ point of intersection at the centroid of the part. The X, Y, and Z axes show the principal axes of the ellipsoid. Project Lead The Way® Copyright 2006

Mass Property Analysis Introduction to Engineering Design Unit 3 – Lesson 3.3 – Structural Analysis Sources Brodinski, K. G. (1989). Engineering materials properties and selection. Prentice Hall, Inc.: Englewood Cliffs, NJ. Budinski, K. G. (1992). Engineering materials (4th Ed.). Prentice Hall, Inc.: Englewood Cliffs, NJ. Gere, J. M., & Timoshenko, S. P. (1997). Mechanics of materials. PWS Publishing Company: Boston. Lockhart, S. D., & Johnson, C. M. (1999). Engineering design communication: Conveying design through graphics (Preliminary Ed.). Addison Wesley Longman, Inc.: Reading, MA. Madsen, D. A., Shumaker, T. M., Turpin, J. L., & Stark, C. (1994). Engineering design and drawing (2nd Ed.). Delmar Publishers Inc.: Albany. Project Lead The Way® Copyright 2006